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Researcher profile

Takashi Matsubara

Takashi Matsubara contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Artificial IntelligenceMachine Learningmath.DSmath-phmath.MPphysics.comp-ph

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Published work

3 published item(s)

preprint2026arXiv

Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems

The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard data-driven architectures. In this work, we introduce the Symplectic Neural Operator, a neural operator architecture designed to preserve the symplectic structure intrinsic to Hamiltonian PDEs. We provide a theoretical characterization of their symplecticity and establish a rigorous long-term stability result based on the combination of symplectic structure preservation and learning accuracy. Numerical experiments on canonical Hamiltonian PDEs corroborate this theoretical result and show that SNOs exhibit improved energy behavior compared with non-structure-preserving neural operators.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Cancer Subtyping by Improved Transcriptomic Features Using Vector Quantized Variational Autoencoder

Defining and separating cancer subtypes is essential for facilitating personalized therapy modality and prognosis of patients. The definition of subtypes has been constantly recalibrated as a result of our deepened understanding. During this recalibration, researchers often rely on clustering of cancer data to provide an intuitive visual reference that could reveal the intrinsic characteristics of subtypes. The data being clustered are often omics data such as transcriptomics that have strong correlations to the underlying biological mechanism. However, while existing studies have shown promising results, they suffer from issues associated with omics data: sample scarcity and high dimensionality. As such, existing methods often impose unrealistic assumptions to extract useful features from the data while avoiding overfitting to spurious correlations. In this paper, we propose to leverage a recent strong generative model, Vector Quantized Variational AutoEncoder (VQ-VAE), to tackle the data issues and extract informative latent features that are crucial to the quality of subsequent clustering by retaining only information relevant to reconstructing the input. VQ-VAE does not impose strict assumptions and hence its latent features are better representations of the input, capable of yielding superior clustering performance with any mainstream clustering method. Extensive experiments and medical analysis on multiple datasets comprising 10 distinct cancers demonstrate the VQ-VAE clustering results can significantly and robustly improve prognosis over prevalent subtyping systems.

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preprint2022arXiv

KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Loss

Many physical phenomena are described by Hamiltonian mechanics using an energy function (the Hamiltonian). Recently, the Hamiltonian neural network, which approximates the Hamiltonian as a neural network, and its extensions have attracted much attention. This is a very powerful method, but its use in theoretical studies remains limited. In this study, by combining the statistical learning theory and Kolmogorov-Arnold-Moser (KAM) theory, we provide a theoretical analysis of the behavior of Hamiltonian neural networks when the learning error is not completely zero. A Hamiltonian neural network with non-zero errors can be considered as a perturbation from the true dynamics, and the perturbation theory of the Hamilton equation is widely known as the KAM theory. To apply the KAM theory, we provide a generalization error bound for Hamiltonian neural networks by deriving an estimate of the covering number of the gradient of the multi-layer perceptron, which is the key ingredient of the model. This error bound gives an $L^\infty$ bound on the Hamiltonian that is required in the application of the KAM theory.

0 citations0 reviewsNo code linkedOpen access